Problems involving movement on water. Problems on movement on water Speed ​​of a boat on a lake in still water

This material is a system of tasks on the topic “Movement”.

Goal: to help students more fully master the technology of solving problems on this topic.

Problems involving movement on water.

Very often a person has to move on water: a river, lake, sea.

At first he did it himself, then rafts, boats, and sailing ships appeared. With the development of technology, steamships, motor ships, and nuclear powered ships came to the aid of man. And he was always interested in the length of the path and the time spent on overcoming it.

Let's imagine that it's spring outside. The sun melted the snow. Puddles appeared and streams ran. Let's make two paper boats and launch one of them into a puddle, and the second into a stream. What will happen to each of the boats?

In a puddle the boat will stand still, but in a stream it will float, since the water in it “runs” to more low place and carries it with him. The same thing will happen with a raft or boat.

In a lake they will stand still, but in a river they will float.

Let's consider the first option: a puddle and a lake. The water in them does not move and is called standing.

The ship will float across the puddle only if we push it or if the wind blows. And the boat will begin to move in the lake with the help of oars or if it is equipped with a motor, that is, due to its speed. This movement is called movement in standing water .

Is it different from driving on the road? Answer: no. This means that you and I know how to act in this case.

Problem 1. The speed of the boat on the lake is 16 km/h.

Which the path will pass boat in 3 hours?

Answer: 48 km.

It should be remembered that the speed of a boat in still water is called own speed.

Problem 2. A motor boat sailed 60 km across a lake in 4 hours.

Find the motorboat's own speed.

Answer: 15 km/h.

Problem 3. How long will it take a boat whose own speed

equal to 28 km/h to swim 84 km across the lake?

Answer: 3 hours.

So, To find the length of the path traveled, you need to multiply the speed by the time.

To find the speed, you need to divide the path length by the time.

To find the time, you need to divide the path length by the speed.

Let's remember the paper boat in the stream. He swam because the water in him moved.

This movement is called going with the flow. And in reverse side – moving against the current.

So, the water in the river moves, which means it has its own speed. And they call her river flow speed. (How to measure it?)

Problem 4. The speed of the river is 2 km/h. How many kilometers does the river carry?

any object (wood chips, raft, boat) in 1 hour, in 4 hours?

Answer: 2 km/h, 8 km/h.

Each of you has swam in the river and remembers that it is much easier to swim with the current than against the current. Why? Because the river “helps” you to swim in one direction, and “gets in the way” in the other.

Those who cannot swim can imagine a situation when a strong wind blows. Let's consider two cases:

1) the wind is blowing at your back,

2) the wind blows in your face.

In both cases it is difficult to go. The wind at our back makes us run, which means our speed increases. The wind in our faces knocks us down and slows us down. The speed decreases.

Let's focus on moving along the river. We have already talked about a paper boat in a spring stream. The water will carry it along with it. And the boat, launched into the water, will float at the speed of the current. But if it has its own speed, then it will swim even faster.

Therefore, to find the speed of movement along the river, it is necessary to add the boat’s own speed and the speed of the current.

Problem 5. The boat's own speed is 21 km/h, and the speed of the river is 4 km/h. Find the speed of the boat along the river.

Answer: 25 km/h.

Now imagine that the boat must sail against the current of the river. Without a motor or even oars, the current will carry her in the opposite direction. But, if you give the boat its own speed (start the engine or seat the rower), the current will continue to push it back and prevent it from moving forward at its own speed.

That's why To find the speed of the boat against the current, it is necessary to subtract the speed of the current from its own speed.

Problem 6. The speed of the river is 3 km/h, and the boat’s own speed is 17 km/h.

Find the speed of the boat against the current.

Answer: 14 km/h.

Problem 7. The ship's own speed is 47.2 km/h, and the speed of the river is 4.7 km/h. Find the speed of the ship downstream and against the current.

Answer: 51.9 km/h; 42.5 km/h.

Problem 8. The speed of a motor boat downstream is 12.4 km/h. Find the boat's own speed if the speed of the river is 2.8 km/h.

Answer: 9.6 km/h.

Problem 9. The speed of the boat against the current is 10.6 km/h. Find the boat's own speed and the speed along the current if the speed of the river is 2.7 km/h.

Answer: 13.3 km/h; 16 km/h.

Let us introduce the following notation:

V s. - own speed,

V current - flow speed,

V according to flow - speed with the current,

V flow flow - speed against the current.

Then we can write the following formulas:

V no current = V c + V current;

Vnp. flow = V c - V flow;

Let's try to depict this graphically:

Conclusion: the difference in speed along the current and against the current is equal to twice the speed of the current.

Vno current - Vnp. flow = 2 Vflow.

Vflow = (Vflow - Vnp.flow): 2

1) The speed of the boat against the current is 23 km/h, and the speed of the current is 4 km/h.

Find the speed of the boat along the current.

Answer: 31 km/h.

2) The speed of a motor boat along the river is 14 km/h, and the speed of the current is 3 km/h. Find the speed of the boat against the current

Answer: 8 km/h.

Task 10. Determine the speeds and fill out the table:

* - when solving item 6, see Fig. 2.

Answer: 1) 15 and 9; 2) 2 and 21; 3) 4 and 28; 4) 13 and 9; 5)23 and 28; 6) 38 and 4.

Average, minimum and maximum speed of the kayak.

Kayaks are rowing boats with a pointed bow and stern, which today are widely used in tourism, water sports, hunting, family walks and long trips across bodies of water of varying complexity. They are maneuverable, light and easy to control, have low weight, excellent stability and buoyancy. Therefore in last years Many lovers of spending time on the water, who are very interested in the suspension and specifications various models. Not least important is the speed of the kayaks.

It must be said that the speed of such boats is a flexible concept, depending on many factors. It is influenced by the characteristics of the current, the physical qualities of the rowers, the dimensions of the boat, the type of water and much more. Theoretically, it ranges from 4 kilometers per hour to 5 kilometers per hour, but in practice the figures can differ significantly. In fact, the approximate speed of a particular kayak model is important for planning routes, and beginners usually focus on tests of single, double, and triple kayaks of various designs. But this is just conditional data that was obtained by passing identical short distances with different kayaks. And on long journeys they can change greatly.

Average kayak speed

Kayaks are rowing boats, which means that their speed is highly dependent on the physical strength and experience of the rowers. Models with a length of 3.5 meters are capable of accelerating to 7 kilometers per hour or more, even if their passengers do not make much effort and row calmly. At the same time, if the rowers are inexperienced and do not know how to stay on course, the boats begin to yaw, and their speed can drop to 3-4 kilometers per hour. In such cases, beginners try to gain it by doing accelerations from time to time, but this often only deprives them of strength and leads to rapid fatigue.

In general, experienced kayakers, when going on long trips, try to maintain an average speed of about 6-7 kilometers per hour. This gives them the opportunity to row for 7-8 hours and still feel quite energetic. Of course, by the end of the movement the speed of the kayak will still drop, but the route will be covered.

It is believed that the average speed of kayaks with two or three oarsmen is higher than that of single-person models. This is true for sports models, but does not always apply to. If a boat goes on a trip with a crew of two or three people, it usually also carries luggage. Under the weight of such a load, the kayak will give a decent draft, the water resistance will increase, therefore, the speed will remain the same. And if the rowers do not know how to work as a team or are very different in physical qualities, it will decrease due to inconsistency of strokes and uncoordinated actions.

Kayak speed in still water

In practice, the speed of a kayak is highly dependent on both the current and the direction of the wind. If the water is still and the weather is calm, one rower without special labor can accelerate the boat up to 7 kilometers per hour, and some models even reach speeds of up to 12 kilometers per hour. We are not talking now about inflatable options without frames, for which 6 kilometers per hour is the limit due to constant yaw. Recently, manufacturers have begun to produce kayaks with hydrofoils or a motor, capable of moving at speeds of up to 40 kilometers per hour!

A quiet view and lack of wind are simply ideal conditions that are not always found. In addition, they often change quickly, so you should always act with speed carefully and take into account the weather and the presence of currents along the route.

Kayak speed with current

The speed of a kayak moving through bodies of water with various types of current depends on its speed and direction. If the boat is moving with the current, its speed often does not matter, and the rowers in this case only have to maneuver. For example, the speed of the river flow is about 20 kilometers per hour. This means that there is no longer a need to add another 5 kilometers of the kayak’s own speed to this value. It is only important to carry out maneuvers correctly so as not to bump into obstacles and shallows. However, you should not count on the boat moving at the speed of the current. It is all kinds of obstacles, rocky shoals that require maneuvering, that can significantly hinder this.

If a kayak is going against a current that is moving more than 2 kilometers per hour, it may not move forward at all. In general, tourists try to avoid such bodies of water, but sometimes such areas come across along the routes. Then the crew disembarks from the boat, leaving equipment and cargo in it, and guides the kayak on a rope or towline. In this case, the boat moves at a speed of approximately 5 kilometers per hour, provided that the shore is sandy or simply hard and level.

Maximum speed of a sports kayak

Sports kayaks are, as a rule, monolithic models that have a streamlined shape and can accommodate from one to three paddlers. They are designed for competitions, so they are fast, lightweight options. On average, such boats reach speeds from 9 kilometers per hour to 12 kilometers per hour, but the maximum records in rowing slalom ranged from 17 to 18 kilometers per hour. Of course, professional athletes who have great experience training. However, ordinary sports kayak owners can reach speeds of up to 15 kilometers per hour over short distances if the boat is moving through suitable water. In this case, it is important to take into account the characteristics of the model and flow, not to try to load it more than the carrying capacity noted in the characteristics, and not to overestimate your own skills and capabilities.